In this section we restrict our study to the groups \(G_2, F_4\)  and \(E_8\) . For \(G=G_2, F_4\)  or \(E_8\) , we have \(G \simeq \operatorname{Aut}G\) , which makes easier our study of Picard-Vessiot extensions and their Galois differential groups. For \(E_6\)  and \(E_7\)  not all real forms are explicitly described. For \(E_6\) , there are 5 real forms, of which 2 are inner. The simply connected form of \(E_6\)  can be seen as the group of transformations of an Albert algebra which leave a certain cubic form invariant. For \(E_7\) , there are 4 real forms, which are all inner. The simply connected form of \(E_7\)  can be seen as the identity component of the group of transformations of an Albert algebra leaving invariant a certain quartic form. The center of this form of \(E_7\)  has order 2 (cf. [1]} 17.7, 17,8).
